Electron states and electron Raman scattering in semiconductor step-quantum well: Electric field effect Ri. Betancourt-Riera a , Re. Betancourt-Riera a, * , L.A. Ferrer-Moreno a , J.M. Nieto Jalil b a Instituto Tecnol ogico de Hermosillo, Avenida Tecnol ogico S/N, Col. Sahuaro, C.P. 83170, Hermosillo Sonora, Mexico b Tecnol ogico de Monterrey-Campus Sonora Norte, Bulevar Enrique Maz on L opez N  965, C.P. 83000, Hermosillo Sonora, Mexico article info Article history: Received 21 December 2016 Received in revised form 25 February 2017 Accepted 25 February 2017 Available online 2 March 2017 Keywords: Electron states Raman scattering Quantum well abstract In this work we determine and show the expressions of the electron states of a step- quantum well with the presence of an external electric field, developed in a GaAs=AlGaAs matrix. The electron states are obtained using the envelope function approximation. In this work it is only necessary to consider a single conduction band, which due to the confinement is divided into a subband system, with T ¼ 0K. Expressions for the electron states and the differential cross-section for an intraband electron Raman scattering process of are presented, the net Raman gain is also calculated. In addition, the interpretation of the singularities found in the emission or excitation spectra is given, since several dispersion configurations are discussed. Furthermore, the effects of an electric field on the electron states and on the differential cross section are studied. © 2017 Elsevier Ltd. All rights reserved. 1. Introduction The nanoscale structures such as quantum wells, dots and wires, have many possible applications, for this reason they have been extensively studied. The introduction of barriers to the movement of charge carriers in semiconductor material gives rise to confinement which causes an enormous amount of quantum effects, especially causing changes in the dynamics of electrons in the system [1e 7]. It is widely known that the Raman scattering experiment can be used to investigate different physical properties of semiconductors nanostructures. The electronic structure of nanostructures can be investigated through Raman scattering processes considering different polarizations of incident and emitted radiation. Furthermore, the calcu- lation of the differential cross-section for an electron Raman scattering process remains an essential tool for the study of semiconductor nanostructures, as it allows correct interpretations of experimental Raman spectra. Nanotechnology allows the creation of devices such as light sources. For instance, light emitting diodes and laser diodes in wide ranges of the electromagnetic spectrum, from terahertz to ultraviolet [8e14]. The applications of these devices cover a wide range of fields in technology, such as optoelectronics, radars and telecommunications [15e17]. One of the semi- conductor nanostructures with greater possibilities of development are the multiple asymmetric quantum wells and espe- cially the step-quantum well. The reason for this is that it allows us to have a relatively simple control of the width of the system and the height of the barrier as well as of other physical parameters; and in this way to be able to create a three-levels system which is necessary for the development of several applications. In recent years, research has been conducted on the * Corresponding author. E-mail address: rbriera@gmail.com (Re. Betancourt-Riera). Contents lists available at ScienceDirect Superlattices and Microstructures journal homepage: www.elsevier.com/locate/superlattices http://dx.doi.org/10.1016/j.spmi.2017.02.049 0749-6036/© 2017 Elsevier Ltd. All rights reserved. Superlattices and Microstructures 104 (2017) 428e437